MinT - Best Known (25−15, 25, s)-Nets in Base 27

Best Known (25−15, 25, s)-Nets in Base 27

(25−15, 25, 94)-Net over F₂₇ — Constructive and digital

Digital (10, 25, 94)-net over F₂₇, using

net from sequence [i] based on digital (10, 93)-sequence over F₂₇, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 10 and N(F) ≥ 94, using
  - a function field by SÃ©mirat [i]

(25−15, 25, 99)-Net over F₂₇ — Digital

Digital (10, 25, 99)-net over F₂₇, using

t-expansion [i] based on digital (9, 25, 99)-net over F₂₇, using
- net from sequence [i] based on digital (9, 98)-sequence over F₂₇, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 9 and N(F) ≥ 99, using
    - a curve from the manYPoints database [i]

(25−15, 25, 116)-Net in Base 27 — Constructive

(10, 25, 116)-net in base 27, using

7 times m-reduction [i] based on (10, 32, 116)-net in base 27, using
- base change [i] based on digital (2, 24, 116)-net over F₈₁, using
  - net from sequence [i] based on digital (2, 115)-sequence over F₈₁, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 2 and N(F) ≥ 116, using
      - a function field by SÃ©mirat [i]

(25−15, 25, 136)-Net in Base 27

(10, 25, 136)-net in base 27, using

3 times m-reduction [i] based on (10, 28, 136)-net in base 27, using
- base change [i] based on digital (3, 21, 136)-net over F₈₁, using
  - net from sequence [i] based on digital (3, 135)-sequence over F₈₁, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 3 and N(F) ≥ 136, using
      - a curve from the manYPoints database [i]

(25−15, 25, 10503)-Net in Base 27 — Upper bound on s

There is no (10, 25, 10504)-net in base 27, because

1 times m-reduction [i] would yield (10, 24, 10504)-net in base 27, but
- the generalized Rao bound for nets shows that 27^mÂ â‰¥ 22532 627871 789681 610746 794150 077473 > 27²⁴ [i]